Characteristic polynomials of random truncations: moments, duality and asymptotics

Autor:	Serebryakov, Alexander, Simm, Nick, Dubach, Guillaume
Rok vydání:	2021
Předmět:	Mathematical Physics Mathematics - Probability 15B52 60B20
Druh dokumentu:	Working Paper
Popis:	We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle. Comment: 19 pages. This version includes an Appendix by Guillaume Dubach
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.10331 Zobrazit plný text záznamu View this record from Arxiv